Problem: Simplify the following expression: $a = \dfrac{-3z^3}{-18z^3 - 30z^2}$ You can assume $z \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-3z^3 = - (3 \cdot z \cdot z \cdot z)$ The denominator can be factored: $-18z^3 - 30z^2 = - (2\cdot3\cdot3 \cdot z \cdot z \cdot z) - (2\cdot3\cdot5 \cdot z \cdot z)$ The greatest common factor of all the terms is $3z^2$ Factoring out $3z^2$ gives us: $a = \dfrac{(3z^2)(-z)}{(3z^2)(-6z - 10)}$ Dividing both the numerator and denominator by $3z^2$ gives: $a = \dfrac{-z}{-6z - 10}$